Multiple choice

'O' is a centre of a circle, AC is a tangent to a circle at point A. If $\Delta$OAC is an isosceles triangle, then find the measure of $\angle$OCA

  1. $75^{o}$
  2. $50^{o}$
  3. $45^{o}$
  4. $40^{o}$
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C Correct answer
Explanation

A tangent at A is perpendicular to the radius OA, so angle OAC = 90 degrees. If triangle OAC is isosceles, the other two angles must be 45 degrees each (since the angle at A is 90).

AI explanation

Because AC is a tangent to the circle at point A and O is the center, the radius OA is perpendicular to the tangent line AC. This means angle OAC is 90 degrees. Since triangle OAC is given as an isosceles triangle and cannot have two 90-degree angles, the sides OA and OC must be equal, making angle OCA equal to angle OAC. Therefore, the measure of angle OCA is 45 degrees.

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